Oedipus Rex is a classic Greek epic, so it makes sense that his name would come from the Greek language.

According to Wikipedia, Oedipus means "swollen foot" and originated from the Greek word "Oidípous". According to legend, when Oedipus was born, his parents sent him away to avoid a prophecy which said he would one day kill his father and marry his mother. Before he was adopted, Oedipus sustained injuries to his feet and ankles, causing him to swell - thus his name.

Rex means "reigning king" which is proven when the prophecy sadly comes true when Oedipus does eventually kill his father and become king.